Results 21 to 30 of about 4,516,797 (266)
Stability of the Cauchy-Jensen Functional Equation in C∗-Algebras: A Fixed Point Approach
Fixed Point Theory and Applications, 2008 we prove the Hyers-Ulam-Rassias stability of C∗-algebra homomorphisms and of generalized derivations on C∗-algebras for the following Cauchy-Jensen functional equation 2f((x+y)/2+z)=f(x)+f(y)+2f(z), which was introduced and investigated by Baak
Jong Su An, Choonkil Park
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Asymptotic behaviour of the solution of a functional-differential equation [PDF]
, 1984 The asymptotic behaviour as t→∞ of the solution of the functional- differential equation y'(t) = -y(t/k), with y(0) = 1 and k > 1 , is derived from an integral representation by the method of steepest descents.
Tripp, CE
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Some hyperstability and stability results for the Cauchy and Jensen equations
Journal of Inequalities and Applications, 2022 In this paper we give some hyperstability and stability results for the Cauchy and Jensen functional equations on restricted domains. We provide a simple and short proof for Brzdȩk’s result concerning a hyperstability result for the Cauchy equation.
Mohammad Bagher Moghimi, Abbas Najati
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On Jensen’s and the quadratic functional equations with involutions [PDF]
Proyecciones (Antofagasta), 2017 We determine the Solutions f : S → H of the generalized Jensen’s functional equation f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ Sand the solutions f : S → H of the generalized quadratic functional equationf ( x + σ(y)) + f (x + τ(y)) = 2f (x) + 2f (y), x, y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Fadli, B. +3 more
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A Variant of Jensen’s Functional Equation on Semigroups
Demonstratio Mathematica, 2016 Abstract We determine the solutions f : S → H of the following functional equation f(xy) + f(σ(y)x) = 2f(x); x; y ∈ S; and the solutions f1; f2; f3 : M → H of the functional equation f1(xy) + f2(σ(y)x) = 2f31(x); x; y ∈ M; where S is a semigroup, M is a monoid, H is an abelian ...
B. Fadli, Driss Zeglami, Samir Kabbaj
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Jensen’s and the quadratic functional equations with an endomorphism [PDF]
Proyecciones (Antofagasta), 2017 We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Sabour, KH, Kabbaj, S
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A Fixed Point Approach to the Stability of Quadratic Functional Equation with Involution
Fixed Point Theory and Applications, 2008 Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we will adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation
Zoon-Hee Lee, Soon-Mo Jung
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On Jensen's functional equation
Aequationes Mathematicae, 1992 The following is offered as main result. Let \((G,\cdot)\) and \((H,+)\) be abelian groups, and \(e\) the neutral element of \((G,\cdot)\). The solutions \(f: G\to H\) of \(f(xy)+f(xy^{-1})=2f(x)\), \(f(e)=0\) are exactly the homomorphisms of \(G\to H\) if, and only if, either \(H\) has no element of order 2 or \([G:G^ 2]\leq 2\), where \(G^ 2:=\{x^ 2 ...
Vasudeva, H.L., Parnami, J.C.
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Fuzzy Stability of Quadratic Functional Equations
Advances in Difference Equations, 2010 The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al.
Dong Yun Shin +3 more
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Functional Differential Equations and Jensen’s Inequality [PDF]
Journal of Mathematical Analysis and Applications, 1987 The authors study various types of stability of the functional differential equations \(x'(t)=F(t,x_ t)\) where \(x_ t(s)=x(t+s),\)- h\(\leq s\leq 0\), and h is a positive constant. The main tool is the Lyapunov functionals. These functionals satisfy certain conditions involving functions which verify Jensen's inequality.
Becker, Leigh C +2 more
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